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No matter how many friends you have on Facebook and MySpace, you won't have more real-life friends than the average person. Using mathematics to model online social networks is an evolving field, with techniques that have been used to model human interaction, such as network modelling, moving into the online world. Users of online social networks tend to build up long lists of "friends" with
whom they only occasionally interact, if at all. Given that we can maintain more weak relationships online than we can in real-life, it is an interesting question to ask whether or not online social networks create as many close friendships as in real life. According to Will Reader of Sheffield Hallam University, the answer is no, and in this there is an interesting scientific and social point to
be found.

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If we are to believe the latest signs from outer space, the local aliens are keen mathematicians. A new crop circle appeared on the 1st of June this year in a barley field near Barbury Castle in Wiltshire, England, measuring 150 feet in diameter and correctly representing the first 10 digits of the irrational constant pi.

The 2008 Plus new writers award has been run and won. This year's competition saw an exceptional standard of writing. The winning entries include biographies of two of the greatest mathematicians of the last 100 years, as well as articles on the mathematics of Google, ants that do maths, why we should (or should not) woo brunettes, the dangers of probing the infinite, and joining the
mathematical mile-high club...

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Maths has long been a theme in the movies. Plus talks to Madeleine Shepherd, organiser of the maths film festival at the recent Edinburgh science festival, about how maths has been presented in the movies over the years, with particular reference to three more recent films, Cube, Pi and Flatland. For more on maths in the movies read the Plus article Maths, madness and movies.

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The Fourier transform is a piece of maths that is, almost single-handedly, responsible for the digital revolution. Digital music and images would be impossible without it, and it has applications in anything from medical imaging to landmine detection. We asked Chris Budd what the Fourier transform does, and how it does it. This podcast accompanies the Plus article Saving lives: The mathematics of tomography.